Magnetic domain walls (DWs) are of great interest both from a theoretical perspective and for applications, especially in the context of innovative magnetic storages [1]}. Recent developments in controlled movement of DWs via spin-polarized current pulses in nanomagnetic structures, in particular in nanowires, are thought to lead to a new class of potential non-volatile storage memories, e.g. racetrack memory [1]}, [3]}, [4]}, [5]}. These devices make use of the fact that spin-transfer driven effects can change the dynamics in sufficiently small ferromagnetic structures (e.g. nanowires), where regions of uniform magnetization, separated by DWs, can appear [6]}, [7]}, [8]}. This motivates further studies of the existence of magnetic domains and their interaction with spin-polarized currents as a building block for the theory in this context. In this paper we take a mathematical perspective and, in a model for nanomagnetic wires, rigorously study the existence of DWs. This led us to discover an apparently new kind of DWs with a certain inhomogeneous and oscillatory structure as explained in more detail below.
